Which two numbers are both square and cube numbers?

The correct answer is Option (4) → 1 and 64

A number that is both a square and a cube is a sixth power, because it must be some number multiplied by itself in pairs and in threes at the same time.

• 1 is both \(1^2\) and \(1^3\), the sixth power \(1^6\)

• 64 is both \(8^2\) and \(4^3\), the sixth power \(2^6\)

The other numbers in the options fail: 8 and 27 are cubes (\(2^3\), \(3^3\)) but not squares.